How planetary growth outperforms migration

Abstract

Planetary migration is a major challenge for planet formation theories. The speed of Type I migration is proportional to the mass of a protoplanet, while the final decade of growth of a pebble-accreting planetary core takes place at a rate that scales with the mass to the two-thirds power. This results in planetary growth tracks (i.e., the evolution of a protoplanet's mass versus its distance from the star) that become increasingly horizontal (migration-dominated) with rising mass of the protoplanet. It has been shown recently that the migration torque on a protoplanet is reduced proportional to the relative height of the gas gap carved by the growing planet. Here we show from 1-D simulations of planet-disc interaction that the mass at which a planet carves a 50% gap is approximately 2.3 times the pebble isolation mass. Our measurements of the pebble isolation mass from 1-D simulations match published 3-D results relatively well, except at very low viscosities where the 3-D pebble isolation mass is significantly higher, possibly due to gap edge instabilities not captured in 1-D. The pebble isolation mass demarks the transition from pebble accretion to gas accretion. Gas accretion to form gas-giant planets therefore takes place over a few astronomical units of migration after reaching first the pebble isolation mass and, shortly after, the 50% gap mass. Our results demonstrate how planetary growth can outperform migration, both during core accretion and during gas accretion, even when the Stokes number of the pebbles is small, St~0.01, and the pebble-to-gas flux ratio in the protoplanetary disc is in the nominal range of 0.01-0.02. We find that planetary growth is very rapid in the first million years of the protoplanetary disc and that the probability for forming gas-giant planets increases with the initial size of the protoplanetary disc and with decreasing turbulent diffusion.